Shampoo in eyes. The eyes are usually quite resilient and this is a really commomplace occurence daily. If the pain or redness does not go away within a day presuming it happened in the morning then you should seek medical evaluation.
No. If it hurts, rinse your eyes with water. A little irritation is expected and will resolve in a day or so.
Probably not needed. Usually all that is necessary is to flush the eyes with water and to allow the natural secretions of the eye wash out the shampoo. If you can sit with your eyes closed this will facilitate this process. At times an ingredient will cause an allergic reaction and the redness may not resolve with just flushing. There are over the counter products that can help and the pharmacist can show you.